Mild cognitive impairment (MCI), characterized by memory impairment but little or no decline in everyday function, is a transitional stage between normal aging and Alzheimer's Disease (AD). Up to 15% of older adults with MCI (oaMCI) convert to AD annually. Few interventions effectively delay cognitive decline and preserve everyday function in oaMCI. However, treatment of comorbid obstructive sleep apnea (OSA) may have potential for delaying cognitive decline. Approximately 60% of older adults with MCI and early AD have OSA, compared to only 7-18% of older adults in the general population.OSA, which is characterized by episodic nocturnal collapse of the upper airway in conjunction with reduction and/or cessation of breathing, causes hypoxia, fragmented sleep, daytime sleepiness, and cognitive dysfunction. OSA is effectively treated with continuous positive airway pressure (CPAP), a pressurized nasal mask worn during sleep, but there is little information on its efficacy in this population. No one has answered the question of whether treatment of OSA in oaMCI with CPAP delays cognitive decline and preserves everyday function. In Aim 1 we will conduct a 6-month randomized controlled pilot clinical trial to estimate the effect size associated with active CPAP (n=75) compared to sham CPAP (n=35) on cognitive and everyday function in older adults with amnestic mild cognitive impairment and OSA. We then propose to follow the active CPAP group for 6 additional months in an open-label trial to estimate the effect size associated with CPAP treatment adherence on cognitive and everyday function. CPAP adherence can be measured precisely with a hidden sensor that determines hours of use at prescribed pressure. In Aim 2 we will explore whether CPAP treatment adherence, controlling for OSA severity at baseline, neuroimaging evidence of pre-existing cerebrovascular disease and hypoxic ischemic brain injury, ApoE4, and previously identified demographic and other patient factors, predicts cognitive and everyday function after 1 year of active CPAP. Aim 3 will determine the feasibility of our participant recruitment and retention plans and other study methods to inform a full-scale trial. Aim 4 will explore the validity of neuroimaging for quantifying the effects of CPAP on the brain by correlating 1 year changes in neuroimaging biomarkers [hippocampal volume (primary), regional brain volume and thickness, hippocampal subfield volumes, ischemic lesion volume, and cerebral blood flow], with 1 year clinical changes. These results will inform the neuroimaging outcome measures for a full-scale trial. The primary goal of the proposed research is to determine effect size and the feasibility of the study design and methods for a full-scale trial that will determine whether treatment of OSA in oaMCI delays cognitive decline and preserves everyday function. Additional potential study benefits are increased understanding of the physiological mechanisms for cognitive decline in oaMCI and OSA, and the characteristics of those most likely to benefit from this treatment.